梯度下降法-python代碼

一個通過迭代求解convex function最小值的方法: Gradient descent(梯度下降法)

http://en.wikipedia.org/wiki/Gradient_descent

這裡給出一個python的代碼:

The gradient descent algorithm is applied to find a local minimum of the function f(x)=x^{4-3x3+2
, with derivative f'(x)=4x3-9x2.
Here is an implementation in the Python
programming language.}

# From
calculation, we expect that the local minimum occurs at x=9/4


xOld = 0

xNew = 6 # The
algorithm starts at x=6
eps = 0.01 # step
size
precision = 0.00001

def f_prime(x):
return 4 * x**3 - 9 * x**2

while abs(xNew - xOld) > precision:

xOld = xNew

xNew = xOld - eps * f_prime(xNew)
print("Local
minimum occurs at ",
xNew)